“excercising faith is a work, no? it’s something you are doing.”
I’m not sure what your point is. Eph 2:8,9 makes it clear that outward works are not necessary for salvation - only faith. Whether or not you think faith is a work doesn’t impact the statement that outward works don’t have anything to do with salvation.
the point is, baptism is not a “work”
a “work” is something you do, and yes, excercising faith is a work by definition.
no one can baptize themself, baptism is something done TO you, not done BY you.